Horowitz and Myers postulated that the Horowitz-Myers geon is the ground state for a conjectural non-supersymmetric AdS/CFT correspondence [1]}. More precisely, let \((M,g)\)  be an asymptotically hyperbolic manifold with toroidal conformal infinity and scalar curvature greater than or equal to \(-n(n+1)\) . Then the total mass is at least equal to the mass of the Horowitz-Myers geon. Moreover, the rigidity holds if and only if \((M,g)\)  is isometric to the Horowitz-Myers geon. Progress on the Horowitz-Myers conjecture has been very limited. For small perturbations of Horowitz-Myers the conjecture was proven by Constable and Myers [2]} and Woolgar proved the rigidity of this conjecture in 3 dimensions [3]}. Recently, a Minkowski-type inequality was proved on the Horowitz-Myers geon by Alaee and the second author [4]}. In this paper, we consider its generalization to the AdS soliton coupled with a Maxwell field. Such a spacetime is called called the AdS-Melvin spacetime and we give a short description in the next paragraph.
